IBDP Mathematics Applications & Interpretations HL Chapter 8 Notes

modelling real life phenomena


These notes have specially been curated by expert teachers to simplify and enlighten concepts given in IB Mathematics HL. The notes are comprehensive in nature and are sufficient to study the chapter in depth and one need not look for other resources beyond the notes provided on our website which can be accessed for free. The notes for Mathematics IBDP HL are available on our official website and can be downloaded for free. You are one click away from obtaining all that you need to score well in IB Mathematics HL.

All DP mathematics courses serve to accommodate the diverse range of needs, interests and abilities of students, and to fulfill the requirements of various university and career aspirations. The aims of these courses are to enable students to: develop mathematical knowledge, concepts, principles, logical, critical and creative thinking, employ and refine their powers of abstraction and generalization. Students are also encouraged to appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives.

This chapter explains how we can apply mathematics to real-world problems to help us understand the world better. A mathematical model is a simplified description of a real system using mathematical concepts and language. The process of developing this model is called mathematical modelling. The modelling cycle involves five steps. First, pose a real-world problem. Then develop a model which represents the problem with mathematics. Test the model by comparing its predictions with known data. Reflect and apply to the original problem and finally extend it. The second topic is linear models. This topic shows how two variables are linearly related if the graph connecting them is a single line. The third topic is a piecewise model. This involves dividing the domain into smaller subintervals, and building a function using a separate formula for each subinterval, rather than using one single formula as it can be insufficient. In the final topic, we solve for unknown parameters by substituting points from known data values to construct a system of equations. By solving these systems of equations, we obtain the parameters which complete the model.
We learn to model various types of functions such as quadratic, cubic and linear. In exponential functions you will learn to graph exponential equations on a graphing calculator, you will learn about asymptotes and investigating slopes. Growth and Decay will look at situations where quantities are either increasing or decreasing exponentially. You will also come to understand that logarithmic functions are used for graphing.